Let P=log_(a)b, where P=log_(2)3*log_(3)4*log_(4)5...log_(2008)2009 and a and b are relatively prime positive integers. Find the smallest possible value of a+b.
P=log_(2)3*log_(3)4*log_(4)5...log_(2008)2009=Log(2009) / Log(2)
+389 
